-Does anyone know if the Coast Guard Reserve would also require information on an Article 15, given that it is an Agency of DHS vice Defense? -Would joining the Public Health Service also allow me to continue "Uniformed Service" without having to pay a deposit (as with Federal Govt jobs) to "buy back" my time? -How long does an Article 15 stay in your military record (or, perhaps more accurately, follow you around) for purposes of guard/reserve, sister service duty?

The Art. 15 stays in the record unless ordered removed by a Board for Correction of Military Records.
It is my understanding that in applying for the USPHS they would want to know about prior disciplinary actions, such as an Art. 15. It would potentially impact the "suitability" requirement for acceptance.
Which security-related situations or circumstances could potentially be disqualifying for active duty commissioning?

Military Discharges: Other than Honorable (Includes a character review and further assessment of separation and reenlistment codes).
Military disciplinary proceedings/court martial.
Employment: Fired, quit, or left under unfavorable circumstances.
Financial: Delinquent on any debt. [Foreclosures, Federal and State tax liens, unpaid child support, student loans (does not include forbearance or deferment), bankruptcy require court documentation; all other accounts must be up to date].
Recent illegal drug use; possession or distribution charges/convictions.
Alcohol related charges/convictions.
Violence/domestic violence charges/convictions.
Felony criminal charges/convictions.
Civil court actions.
Pending criminal charges/convictions.

Don't know about the buy back question.
What effect it would have with a USPHS application would depend on what the 15 was for and how long ago it is alleged to have happened.

Once an Article 15 is recorded in your permanent personnel file, it is presumed to be administratively and substantively correct. Thereafter, the burden of proof rests with you to provide evidence of a clear and convincing nature that the Article 15 was either unwarranted, unfounded, or unjust, in whole or in part, thereby warranting removal. I can help you file an appeal to have the Article 15 removed from your record. Feel free to give me a call to discuss further- initial consultation is always free. Good luck.